Quantum thermal transistor performance under fixed-temperature baths: A Langevin framework for spectral and noise modeling

Advanced thermal management is vital for reliable electronics, and quantum thermal transistors (QTTs) offer a novel solution using quantum mechanical states to control heat like electric current. They offer the potential to be used in thermal circuits that enhance thermal management capabilities. Despite substantial theoretical progress, practical realization faces challenges due to scalability, environmental interactions, and the influence of noise. In this work, we investigate the role of stochastic dynamics and thermal noise in QTTs through a framework based on the Heisenberg picture and quantum Langevin equations. We develop a Langevin-based model in which fluctuations in thermal baths are represented as noise, enabling a different approach to modeling system-bath interactions and energy flow in a QTT. Unlike previous approaches formulated in the Schr"odinger picture, our method captures the impact of the spectral properties of the thermal baths on transistor characteristics such as energy flow variation and amplification rate. We define the heat flow in terms of system observables, offering a measurable framework for describing heat transfer. We characterize the noise spectral density of the thermal baths and analyze transistor characteristics across Ohmic, sub-Ohmic, and super-Ohmic regimes. We also demonstrate how this model extends beyond the Markovian limit, enabling exploration of non-Markovian effects. Furthermore, we show that our model recovers the Lindblad master equation bridging the Heisenberg and Schr"odinger approaches. Our results highlight the importance of incorporating noise and spectral modeling to accurately describe and optimize the performance of QTTs, paving the way for more realistic device-level implementations in quantum thermal management.